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Production-process modelling based on production-management data: a Petri-net approach

TL;DR: This paper describes how to apply timed Petri nets and existing production data to the modelling of production systems and describes a method for using these data to construct a Petri-net model algorithmically.
Abstract: During the development of a production control system, an appropriate model of the production process is needed to evaluate the various control strategies. This paper describes how to apply timed Petri nets and existing production data to the modelling of production systems. Information concerning the structure of a production facility and the products that can be produced is usually given in production-data management systems. We describe a method for using these data to construct a Petri-net model algorithmically. The timed Petri-net simulator, which was constructed in Matlab, is also described. This simulator makes it possible to introduce heuristics, and, in this way, various production scenarios can be evaluated. To demonstrate the applicability of our approach, we applied it to a scheduling problem in the production of furniture fittings.

Summary (3 min read)

1. Introduction

  • As the role played by information systems in production control increases, the need for a proper evaluation of the various decisions in both the design and operational stages of such systems is becoming more and more important.
  • In section 3 the method for modelling the production system using data from the production-management system is presented.

2. Timed Petri nets

  • Petri nets are a graphical and mathematical modelling tool that can be used to study systems that are characterized as being concurrent and asynchronous.
  • A situation where conflict and concurrency are mixed is called a confusion.
  • With enabling durations the firing of the transitions happens immediately and the time delays are represented by forcing transitions that are enabled to stay so for a specified period of time before they can fire.
  • By using holding durations the formal representation of the timed Petri net is extended with the information of time, represented by the multiple TPN ¼ ðP;T; I;O; s0; fÞ; where P, T, I, O are the same as above, s0 is the initial state of the timed Petri net, and f : T !.

3. The modelling of production systems

  • This section deals with models for production facilities.
  • These models play a role in the design and the operational control of a plant.
  • If used in all stages, an additional benefit of improving the communication between these stages is achieved.
  • And the structure of the model is derived from existing production-management data (Wortmann 1995).
  • A method for recognizing basic production elements from the management system’s database is provided.

3.1. The class of production system

  • With the method presented here, several scheduling problems that appear in production systems can be solved.
  • Different jobs are needed to produce a desired product.
  • Each resource can process a limited number of operations.
  • This limitation is defined by the capacity of resources. .
  • Work orders define the quantity of desired products and the starting times.

3.2. The modelling of production activities

  • First, a method of describing the production-system activities with timed Petri nets using the holding-duration representation of time is presented.
  • When the resource is used at the start of the operation the unavailable token appears in place p1op.
  • A particular operation can often be performed on different (sets of) resources with different availability, and the time duration can be different on each set of resources.
  • If the operation chooses resource R3, its time duration is determined by the transition t2in¼ td2.
  • An example of two successive operations is shown in figure 6, depicted as Op1 and Op2.

3.3. Modelling using the data from production-management systems

  • The most widely used production-management information system in practice is MRP II.
  • Table 1 shows an example of a BOM describing the production of product I, which is composed of two components, i.e. three items of J and and two items of K.
  • The PN structure in figure 9 is achieved if the sequence of operations described by the routing table (table 2) is modelled.
  • The procedure of each simulation step computes a new state skþ1¼ (mkþ1, nkþ1, rkþ1) of a timed Petri net in the next calculation interval.
  • In the next stage the clocks for each token have to be determined rkþ1(pi).

5. Case study: the production of furniture fittings

  • The applicability of their approach will be demonstrated on a model of a production system where furniture fittings are produced.
  • The production system is divided into a number of departments.
  • To implement a detailed schedule, how the work should be done, an additional scheduling system should be implemented.
  • The process under consideration is an assembly process where different finished products are assembled from a number of sub-items.
  • A description of the data presented in the table will be given later during the modelling procedure.

5.1. Modelling

  • Data from the BOM and the routings were used to build a Petri-net model.
  • As the authors can see from table 3, there are two work orders: the first has to start immediately with its production, while the starting time of the second is 80 time units later.
  • The first operation in this table (Op1) shows that the sub-items should be produced first as prescribed by ‘BOM_CCL’.
  • There is one operation needed to produce the subitem ‘Screw’, two operations to produce ‘Nut’ and ‘Clamp’, and three operations to produce the ‘Angle-bar with holder L’.
  • Finally, the resulting model is verified using P-invariant analysis.

5.2. Results

  • The scheduling problem was mapped onto timed Petri nets, and the assembly process was modelled with timed Petri nets.
  • The authors tested different priority rules (SPT, LPT, etc.) and different schedules were achieved.
  • It respects all the production constraints and the duration of the whole process can be identified.
  • The PN-based heuristic search method of Lee and DiCesare (1994) was programmed in Matlab and used with a slightly modified heuristic function, as proposed by Yu et al. (2003b): hðmÞ ¼ w0 Op depthðmÞ.
  • The result using this tool is presented in figure 18.

6. Conclusion

  • To be able to analyse a production system, a mathematical model of the system is required.
  • The production data are given with the BOM and the routings.
  • For the particular timed Petri net the authors present a simulator that can be used to simulate models built with timed Petri nets.
  • The applicability of the proposed approach was illustrated for an assembly process for producing furniture fittings.
  • The model developed with the proposed method was used to determine a schedule for production operations.

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Production-process modelling based on production-management
data: a Petri-net approach
D. GRADIS
ˇ
AR*{{ and G. MUS
ˇ
IC
ˇ
{
{Faculty of Electrical Engineering, University of Ljubljana, Trzˇ as
ˇ
ka 25, 1000 Ljubljana, Slovenia
{Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
During the development of a production control system, an appropriate model of the
production process is needed to evaluate the various control strategies. This paper
describes how to apply timed Petri nets and existing production data to the modelling of
production systems. Information concerning the structure of a production facility and the
products that can be produced is usually given in production-data management systems.
We describe a method for using these data to construct a Petri-net model algorithmically.
The timed Petri-net simulator, which was constructed in Matlab, is also described. This
simulator makes it possible to introduce heuristics, and, in this way, various production
scenarios can be evaluated. To demonstrate the applicability of our approach, we applied
it to a scheduling problem in the production of furniture fittings.
Keywords: Timed Petri nets; Modelling; Scheduling; Production systems; Simulation
1. Introduction
As the role played by information systems in production
control increases, the need for a proper evaluation of the
various decisions in both the design and operational stages
of such systems is becoming more and more important.
In general, an appropriate model of a production process
is needed in order to cope with its behaviour. However, this
behaviour is often extremely complex. When the behaviour
is described by a mathematical model, formal methods can
be used, which usually improve the understanding of
systems, allow their analysis and help in implementation.
Within the changing production environment the effective-
ness of production modelling is, therefore, a prerequisite
for the effective design and operation of manufacturing
systems.
Scheduling is a fundamental problem in the control of
any resource-sharing organization. Scheduling problems
are very complex and many have been proven to be NP
hard (Jain and Meeran 1999). There are several major
approaches to scheduling. Formal, theoretically oriented
approaches have to ignore many practical constraints in
order to solve these problems efficiently (Richard and
Proust 1998). This is the reason why only a few real
applications exist in the industrial environment (Hauptman
and Jovan 2004). Mathematical programming approaches
are computationally demanding and often cannot achieve
feasible solutions to practical problems (Jain and Meeran
1999). Soft-computing approaches, e.g. genetic algorithms
and neural networks, require considerable computation
and only yield sub-optimal solutions. Instead, heuristic
dispatching rules (Panwalker and Iskaneder 1977,
Blackstone et al. 1982), such as Shortest Processing Time
(SPT) or Longest Processing Time (LPT), are commonly
used in practice. An interesting property of heuristic
dispatching rules is that they can easily be used in
conjunction with production models derived within differ-
ent mathematical modelling frameworks, e.g. the disjunc-
tive graph model (Bła
_
zewicz et al. 1996, 2000), timed
automata (Abdeddaim et al. 2006), and Petri nets (Murata
1989, Zhou and Venkatesh 1999).
Petri nets (PN) represent a powerful graphical and
mathematical modelling tool. The different abstraction
levels of Petri-net models and their different interpretations
make them especially usable for life-cycle design (Silva and
Teruel 1997). Many different extensions of classical Petri
*Corresponding author. Email: dejan.gradisar@ijs.si
International Journal of Computer Integrated Manufacturing, Vol. 00, No. 0, Month 2007, 1 17
International Journal of Computer Integrated Manufacturing
ISSN 0951-192X print/ISSN 1362-3052 online ª 2007 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/09511920601103064

nets exist, and these are able to model a variety of real
systems. In particular, timed Petri nets can be used to
model and analyse a wide range of concurrent discrete-
event systems (Zuberek 1991, Van der Aalst 1996, Zuberek
and Kubiak 1999, Bowden 2000). Several previous studies
have addressed the timed-Petri-net-based analysis of
discrete-event systems. Lo
´
pez-Mellado (2002), for example,
deals with the simulation of the deterministic timed Petri
net for both timed places and timed transitions by using the
firing-duration concept of time implementation. Van der
Aalst (1998) discusses the use of Petri nets in the context of
workflow management. Gu and Bahri (2002) discuss the
usage of Petri nets in the design and operation of a batch
process. There is a lot of literature on the applicability of
PNs in the modelling, analysis, synthesis and implementa-
tion of systems in the manufacturing-applications domain.
A survey of the research area and a comprehensive biblio-
graphy can be found in Zhou and Venkatesh (1999).
Recalde et al. (2004) give an example-driven tour of Petri
nets and manufacturing systems where the use of Petri-net
production models through several phases of the design
life-cycle is presented.
A straightforward way of using the heuristic rules within
a Petri-net modelling framework is to incorporate the rules
for the conflict-resolution mechanism in an appropriate
Petri-net simulator. Many different Petri-net simulators
exist, some of which also support timed Petri nets, and they
usually support random decisions to make a choice in the
case of conflicts. The Petri-net toolbox for Matlab
(Matcovschi et al. 2003) allows the use of priorities or
probabilities to make a choice about a conflicting transition
to fire. CPN Tools can also be used for the modelling,
simulating and analyses of untimed and timed Petri nets
(Ratzer et al. 2003).
One of the central issues when using Petri nets in
manufacturing is the systematic synthesis of Petri-net
models for automated manufacturing systems. Problems
arise when the complexity of a real-world system leads to a
large Petri net having many places and transitions (Zhou
et al. 1992). A common approach is to model the com-
ponents and build the overall systems in a bottom-up
manner. However, a Petri net constructed by merging
arbitrary sub-nets is difficult to analyse, and, furthermore,
an early design error can lead to an incorrect model. Zhou
et al. (1992) propose a hybrid methodology that builds a
model by combining the top-down refinement of operations
and the bottom-up assignment of resources. Another
approach is the use of well-defined net modules and
restricting their interaction. By merging corresponding
sub-nets in a predefined way a set of desired properties of
the resulting net is maintained (Jeng 1997). But the
synthesis of complex models remains tedious and error-
prone. Therefore, a number of researchers have put toward
the idea of modelling a flexible manufacturing system
(FMS) with a FMS modelling language. The language
model is then automatically translated into one of the
standard PN classes, such as Coloured Petri nets CPN
(Arjona-Suarez and Lopez-Mellado 1996) or Generalized
stochastic Petri nets GSPN (Xue et al. 1998). Some
researchers have also proposed the translation into special
PN classes, e.g. B-nets (Yu et al. 2003a). Other approaches
to the automatic synthesis of PN models are presented by
Camurri et al. (1993), Ezpeleta and Colom (1997) and
Basile et al. (2006) and special PN classes appropriate for
modelling FMS appear in Proth et al. (1997), Van der Aalst
(1998) and Janneck and Esser (2002).
On the other hand, Huang et al. (1995) use a discrete-
event matrix model of a FMS, which can be built based on
standard manufacturing data, and can also be interpreted
as a Petri net. This latter approach is particularly attractive
when there are data concerning the production process
available within some kind of production-management
information system. Using these data, a model-building
algorithm can be embedded within the information system.
In this paper we propose a method for using the data from
management systems, such as Manufacturing Resource
Planning (MRP II) systems (Wortmann 1995), to automate
the procedure of building up the Petri-net model of a
production system. Instead of using a discrete-event matrix
model, the Petri net is built directly in a top-down manner,
starting from the bill of materials (BOM) and the routings
(Wortmann 1995). The BOM and the routing data,
together with the available resources, form the basic
elements of the manufacturing process. These data can be
effectively used to build up a detailed model of the
production system with Petri nets. The product structure
given in the form of the BOM and the process structure in
the form of routings have also been used by other
researchers. Czerwinski and Luh (1994) propose a method
for scheduling products that are related through the BOM
using an improved Lagrangian Relaxation technique. An
approach presented by Yeh (1997) maintains production
data by using a bill of manufacture (BOMfr), which
integrates the BOM and the routing data. Production data
are then used to determine the production jobs that need to
be completed in order to meet demands. Compared to
previous work, the method proposed in this paper builds a
Petri-net model that can be further analysed, simulated and
used for scheduling purposes.
First we define timed Petri nets, where time is introduced
by using the holding-durations concept. A general class of
place/transition (P/T) nets supplemented by timed transi-
tions is used. Although several special classes of PNs have
been defined, there was no need to either restrict the
behaviour of the P/T nets or extend their modelling power
during the work presented in this paper. The use of some
kind of high-level Petri nets would, however, probably be
needed in a real industrial implementation. Practical
2 D. Gradis
ˇ
ar and G. Mus
ˇ
i
c

experience also shows that, for most applications in a real
manufacturing environment, the use of deterministic time
delays is sufficient. Adopting the class of timed P/T nets, a
method for modelling the basic production activities with
such a Petri net is described. A corresponding algorithm of
automatic model building is presented. For a defined, timed
Petri net a simulator was built, for which different heuristic
rules can be introduced for scheduling purposes. The
applicability of the proposed approach was illustrated
using a practical scheduling problem, where data con-
cerning the production facility is given with the BOM and
the routings. The model constructed using the proposed
method was used to determine a schedule for the pro-
duction operations.
In the next section we describe timed Petri nets that can be
used for the modelling and analysis of a production system.
In section 3 the method for modelling the production system
using data from the production-management system is
presented. Section 4 explains the simulator/scheduler that
was built for the purposes of scheduling; it can use different
heuristic dispatching rules. An illustrative application of
modelling an assembly process and developing a schedule
using timed Petri nets is given in section 5. Finally, the
conclusions are presented in section 6.
2. Timed Petri nets
Petri nets are a graphical and mathematical modelling tool
that can be used to study systems that are characterized as
being concurrent and asynchronous.
The basic Place/Transition Petri net (Zhou and
Venkatesh 1999) is represented by the multiple
PN ¼ðP; T; I; O ; M
0
Þ;
where P ¼ {p
1
, p
2
,..., p
g
} is a finite set of places; T ¼ t
1
,
t
2
,...,t
h
is a finite set of transitions; I : ðP TÞ!IN is the
input arc function. If there exists an arc with weight k
connecting p
i
to t
j
, then I(p
i
, t
j
) ¼ k, otherwise I(p
i
, t
j
) ¼ 0;
O : ðP TÞ!IN is the output arc function. If there exists
an arc with weight k connecting t
j
to p
i
, then O(p
i
, t
j
) ¼ k,
otherwise O( p
i
, t
j
) ¼ 0; M : P ! IN is the marking; and M
0
is the initial marking.
Functions I and O define the weights of the directed arcs,
which are represented by numbers placed along the arcs. In
the case when the weight is 1, this marking is omitted, and in
the case when the weight is 0, the arc is omitted. Let .t
j
P
denote the set of places which are inputs to transition t
j
2 T,
i.e. there exists an arc from every p
i
2 .t
j
to t
j
. A transition t
j
is enabled by a given marking if, and only if, M(p
i
) I
(p
i
, t
j
), 8p
i
2 .t
j
. An enabled transition can fire, and as a
result remove tokens from input places and create tokens in
output places. If the transition t
j
fires, then the new marking
is given by M
0
(p
i
) ¼ M(p
i
) þ O(p
i
, t
j
) 7 I(p
i
, t
j
), 8p
i
2 P.
The structure of the Petri net can also be given in a
matrix representation (Zhou and Venkatesh 1999). We
define a g6h input matrix I, whose (i, j) entry is I(p
i
, t
j
).
Similarly, we define an output matrix O of the same
size, whose elements are defined by O(p
i
, t
j
). Matrices I
and O precisely describe the structure of the Petri net
and make it possible to explore the structure using linear
algebraic techniques. Furthermore, the marking vector M
where M
i
¼ M(p
i
), and a firing vector u with a single non-
zero entry u
j
¼ 1, which indicates a transition t
j
that fires,
are defined. Using these matrices we can now write a
state equation M
kþ1
¼ M
k
þ (O 7 I) u
k
. The subscript k
denotes the kth firing in some firing sequence.
An important concept in PNs is that of conflict. Two
events are in conflict if either one of them can occur, but
not both of them. Conflict occurs between transitions
that are enabled by the same marking, where the firing of
one transition disables the other transition. Also, parallel
activities or concurrency can easily be expressed in terms
of a PN. Two events are parallel if both events can
occur in any order without conflicts. A situation
where conflict and concurrency are mixed is called a
confusion.
The concept of time is not explicitly given in the original
definition of Petri nets. However, for the performance
evaluation and scheduling problems of dynamic systems it
is necessary to introduce time delays. Given that a
transition represents an event, it is natural that time delays
should be associated with transitions. Time delays may be
either deterministic or stochastic. In this work, timed Petri
nets with deterministic time delays are used to model the
behaviour of a production system.
As described by Bowden (2000) there are three basic
ways of representing time in Petri nets: firing durations,
holding durations and enabling durations. The firing-
duration principle says that when a transition becomes
enabled it removes the tokens from input places immedi-
ately but does not create output tokens until the firing
duration has elapsed. Zuberek (1991) gives a well-defined
description of this principle. When using the holding-
duration principle, a created token is considered unavail-
able for the time assigned to the transition that created the
token. The unavailable token cannot enable a transition
and therefore causes a delay in the subsequent transition
firings. This principle is graphically represented in figure 1,
where the available tokens are schematized with the
corresponding number of undistinguishable (black) tokens
and the unavailable tokens are indicated by the center not
being filled. The time duration of each transition is given
beside the transition, e.g. f(t
1
) ¼ t
d
. When the time duration
is 0 this denotation is omitted. In figure 1, t denotes a model
time represented by a global clock and t
f
denotes the firing
time of a transition. With enabling durations the firing of
the transitions happens immediately and the time delays are
Production-process modelling based on production-management data 3

represented by forcing transitions that are enabled to stay
so for a specified period of time before they can fire.
Holding durations and firing durations are in fact the
same way of representing time. We prefer the use of holding
durations, because in comparison with firing durations they
do not have transitions that remain active over periods of
time. Thus, the schematics of holding durations are closer
to those of non-timed Petri nets. The main difference
between using holding and enabling durations can be seen
in a Petri net where confusion appears. In this case, more
transitions are enabled by one marking. When the enabling
duration policy is used, the firing of one transition can
interrupt the enabling of other transitions, as the marking,
which has enabled the previous situation, has changed
(Bowden 2000). It is reasonable to use holding durations
when modelling production processes where the operations
are non pre-emptive.
By using holding durations the formal representation of
the timed Petri net is extended with the information of time,
represented by the multiple
TPN ¼ðP; T; I; O; s
0
; fÞ;
where P, T, I, O are the same as above, s
0
is the initial state
of the timed Petri net, and f : T ! IR
þ
0
is the function that
assigns a non-negative deterministic time-delay to every
t
j
2 T. The delays can be represented by 16h row vector f
whose jth entry is f(t
j
).
The state of a timed Petri net is a combination of three
functions
s ¼ðm; n; rÞ;
where m : P ! IN is a marking function of available tokens.
It defines a g61 column vector m whose ith entry is m(p
i
);
n : P ! IN is a marking function of unavailable tokens. It
defines a g6 1 column vector n whose ith entry is n(p
i
); and
r is the remaining-holding-time function that assigns values
to a number of local clocks that measure the remaining
time for each unavailable token (if any) in a place.
Assuming l unavailable tokens in p
i
, i.e. n(p
i
) ¼ l, the
remaining-holding-time function r(p
i
) defines a vector of
l positive real numbers denoted by r(p
i
) ¼ [r(p
i
)[1],
r(p
i
)[2],..., r(p
i
)[l]]; r is empty for every p
i
, where n(p
i
) ¼ 0.
A transition t
j
is enabled by a given marking if, and only
if, m(p
i
) I(p
i
, t
j
), 8 p
i
2 .t
j
. The firing of transitions is
considered to be instantaneous. A new local clock is created
for every newly created token and the initial value of the
clock is determined by the delay of the transition that
created the token. When no transition is enabled, the time
of the global clock is incremented by the value of the
smallest local clock. An unavailable token in a place where
a local clock reaches zero becomes available and the clock
is destroyed. The enabling condition is checked again. The
procedure for determining a new state is described in detail
in section 4.
3. The modelling of production systems
This section deals with models for production facilities.
These models play a role in the design and the operational
control of a plant. Petri nets are a family of tools that
provide a framework or working paradigm which can be
used for many of the problems that appear during the life-
cycle of a production system (Silva and Teruel 1997). If
used in all stages, an additional benefit of improving the
communication between these stages is achieved.
We present a method for modelling production systems
using timed Petri nets based on data from production-
management systems for the purpose of performance
control. Van der Aalst (1996) provides a method for
mapping scheduling problems onto timed Petri nets, where
the standard Petri-net theory can be used. To support the
modelling of scheduling problems, he proposed a method
to map tasks, resources and constraints onto a timed Petri
net. In this paper a different representation of time in Petri
nets is used, and the structure of the model is derived from
existing production-management data (Wortmann 1995). A
method for recognizing basic production elements from the
management system’s database is provided.
When timed Petri nets are used, it is possible to derive
performance measures such as makespan, throughput, pro-
duction rates, and other temporal quantities. In this work
the simulation of a timed Petri net is used to estimate the
performance measures and evaluate different priority rules.
3.1. The class of production system
With the method presented here, several scheduling pro-
blems that appear in production systems can be solved. The
production systems are considered where management
systems (MRP II) are used to plan the production process.
Figure 1. Timed Petri net with holding durations.
4 D. Gradis
ˇ
ar and G. Mus
ˇ
i
c

The system generates work orders that interfere with the
demands for the desired products. Different jobs are needed
to produce a desired product. In general, more operations
have to be performed using different resources in order to
complete a specific job. To complete a specific product,
more sub-products may be needed. The BOM defines a list
of components. These components determine sub-jobs that
are needed to manufacture a parent item. In this way the
general scheduling problem is defined and can be given as:
. n jobs are to be processed: J ¼ {J
j
}, j ¼ 1,..., n;
. m resources are available: M ¼ {M
i
}, i ¼ 1,..., m;
. each job J
i
is composed of n
j
operations: O
j
¼ {o
jk
},
k ¼ 1,..., n
j
;
. each operation can be processed on (more) different
sets of resources S
jkl
2 R; l determines the number of
different sets;
. the processing time of each operation o
jkl
, using
resource set S
jkl
, is defined as T
jkl
;
. precedence constraints are used to define that one job
has to be performed before another.
Using this definition, the following assumptions have to be
considered.
. Resources are always available and never break
down.
. Each resource can process a limited number of
operations. This limitation is defined by the capacity
of resources.
. Operations are non pre-emptive.
. When an operation is performed, it is desirable to
free the resources so that they can become available
as soon as possible. Intermediate buffers between
processes are common solutions.
. Processing times are deterministic and known in
advance.
. Work orders define the quantity of desired products
and the starting times. Orders that are synchronized
in time are considered jointly.
. In the case where a job requires sub-products, for
each of the additions, sub-jobs are to be defined.
3.2. The modelling of production activities
First, a method of describing the production-system
activities with timed Petri nets using the holding-duration
representation of time is presented. The places represent
resources and jobs/operations, and the transitions represent
decisions or rules for resource assignment/release and for
starting/ending jobs.
To make a product, a set of operations has to be per-
formed. We can think of an operation as a set of events and
activities. Using a timed PN, events are represented by
transitions and activity is associated with the presence of a
token in a place.
An elementary operation can be described by one place
and two transitions (see figure 1). When all the input con-
ditions are met (raw material and resources are available)
the event that starts the operation occurs, t
1
. This transition
also determines the processing time of an operation. During
that time the created token is unavailable in place p
2
and
the operation is being executed. After that time the
condition for ending the operation is being satisfied and
t
2
can be fired. Place p
1
is not a part of the operation, it
determines the input condition.
When parallel activities need to be described the Petri-net
structure presented in figure 2 is used. The time delays of
the transitions t
11in
and t
12in
define the duration of each
operation. An available token in place p
11out
(p
12out
)
indicates that the operation is finished. Transition t
1
is
used to synchronize both operations.
An operation might need resources, usually with a
limited capacity, to be executed; this is illustrated in
figure 3. Place p
R1
is used to model a resource. Its capacity
is defined by the initial marking of that place. The resource
is available to process the operation if there are enough
available tokens in it. When the resource is used at the start
of the operation the unavailable token appears in place
p
1op
. After the time defined by transition t
1in
the token
becomes available, t
1out
is fired, and the resource becomes
free to operate on the next job. For this reason, zero time
Figure 2. Two parallel operations.
Figure 3. Operation that uses a resource with finite
capacity.
Production-process modelling based on production-management data 5

Citations
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Journal ArticleDOI
TL;DR: In this paper, a data-based scheduling framework for complex manufacturing systems is proposed and discussed for its implementation into a semiconductor manufacturing system, based on the analysis of the differences and relations between traditional and databased scheduling methods.
Abstract: Based on the analysis of the differences and relations between traditional and data-based scheduling methods for complex manufacturing systems, a data-based scheduling framework was proposed and discussed for its implementation into a semiconductor manufacturing system. The state-of-the-art research on the key technologies of data-based scheduling was then introduced together with their development trends. By taking a real wafer fabrication facility (fab) as an example, an adaptive dispatching rule (ADR) was developed. Firstly, a simulation system for the fab was developed, and study samples were generated by simulation. Then, the relations between the parameters of ADR and real-time running state of the fab were obtained by learning with an integration of a binary regression model, backward propagation neuro-network, and particle swarm optimization algorithm from these study samples to realize the adaptive regulations of these parameters of ADR. Finally, ADR was integrated with the simulation system. The simulation results showed that ADR had a positive effect on the operational performance of the fab. Its “move” performance was increased by 2.41 and 7.24 % for the cases of 70 % and 90 % workload, respectively.

26 citations

Journal ArticleDOI
TL;DR: In this paper, the authors propose a scheduling model for manufacturing systems. But, with the growing complexity of the manufacturing system, traditional schedu- tation models are not suitable for it.
Abstract: Scheduling modeling for manufacturing system has always been a great challenge in both industrial and academic community. With the growing complexity of the manufacturing system, traditional schedu...

21 citations

Journal ArticleDOI
TL;DR: A new computationally effective approach is introduced for designing efficient decision support tools based on the analysis of SSs, in which the computational time is an important requirement to deal with optimal scheduling, routing or planning policies.
Abstract: The state space (SS) analysis of a timed coloured Petri net (TCPN) has been used traditionally for validation and verification of system properties. Performance modelling using TCPN has also received the widespread attention of researchers in recent years as a promising alternative to improve productivity and competitiveness of present flexible manufacturing systems. In this article, a new computationally effective approach is introduced for designing efficient decision support tools based on the analysis of SSs, in which the computational time is an important requirement to deal with optimal scheduling, routing or planning policies. The SS analysis of a system specified in the TCPN formalism is faced with an algorithm in two stages, key implementation algorithmic aspects are considered to improve the time consuming tasks (transition evaluation, data management and information search). In order to provide good benchmarking results when applied to the optimisation of industrial scheduling problems, some examples are given and future work is addressed at the end of the article.

18 citations

Book ChapterDOI
26 Oct 2015
TL;DR: This paper presents how an existing approach to business process management, Subject-oriented BPM (S-BPM), provides a foundation for seamlessly integrating processes in production enterprises, from business processes to real-time production processes.
Abstract: This paper presents how an existing approach to business process management, Subject-oriented BPM (S-BPM), provides a foundation for seamlessly integrating processes in production enterprises, from business processes to real-time production processes. The applicability of S-BPM is based on its simplicity and encapsulation of separate process domains. This supports agility as all stakeholders can be engaged and the effects of changes can be limited to individual modules of the process. An application and tool support developed in an ongoing European research project are presented to illustrate the approach.

17 citations

References
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Journal ArticleDOI
01 Apr 1989
TL;DR: The author proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis, and one section is devoted to marked graphs, the concurrent system model most amenable to analysis.
Abstract: Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

10,755 citations


"Production-process modelling based ..." refers methods in this paper

  • ...…rules is that they can easily be used in conjunction with production models derived within different mathematical modelling frameworks, e.g. the disjunctive graph model (Bła_zewicz et al. 1996, 2000), timed automata (Abdeddaim et al. 2006), and Petri nets (Murata 1989, Zhou and Venkatesh 1999)....

    [...]

Journal ArticleDOI
TL;DR: This paper introduces workflow management as an application domain for Petri nets, presents state-of-the-art results with respect to the verification of workflows, and highlights some Petri-net-based workflow tools.
Abstract: Workflow management promises a new solution to an age-old problem: controlling, monitoring, optimizing and supporting business processes. What is new about workflow management is the explicit representation of the business process logic which allows for computerized support. This paper discusses the use of Petri nets in the context of workflow management. Petri nets are an established tool for modeling and analyzing processes. On the one hand, Petri nets can be used as a design language for the specification of complex workflows. On the other hand, Petri net theory provides for powerful analysis techniques which can be used to verify the correctness of workflow procedures. This paper introduces workflow management as an application domain for Petri nets, presents state-of-the-art results with respect to the verification of workflows, and highlights some Petri-net-based workflow tools.

2,862 citations

Journal ArticleDOI
TL;DR: A summary of over 100 priority dispatching rules, a list of many references that analyze them, and a classification scheme are presented in this article, along with a classification of the rules.
Abstract: In the past two decades researchers in the field of sequencing and scheduling have analyzed several priority dispatching rules through simulation techniques. This paper presents a summary of over 100 such rules, a list of many references that analyze them, and a classification scheme.

1,151 citations

Journal ArticleDOI
TL;DR: A review of the state of the art in the study of dispatching rules can be found in this paper, where a dispatching rule is used to select the next job to be processed from a set of jobs awaiting service.
Abstract: This paper reviews recent studies of dispatching rules. A dispatching rule is used to select the next job to be processed from a set of jobs awaiting service. The paper has two objectives. The first is to discuss the state of the art in the study of dispatching rules. The discussion includes analytical approaches, simulation techniques and evaluation criteria. The second objective of the paper is to compare several of the dispatching rules listed in the Appendix using the results of recently published studies. It is impossible to identify any single rule as the best in all circumstances. However, several rules have been identified as exhibiting good performance in general.

967 citations


"Production-process modelling based ..." refers background in this paper

  • ...Instead, heuristic dispatching rules (Panwalker and Iskaneder 1977, Blackstone et al. 1982), such as Shortest Processing Time (SPT) or Longest Processing Time (LPT), are commonly used in practice....

    [...]

Journal ArticleDOI
TL;DR: A subclass of the deterministic job-shop scheduling problem in which the objective is minimising makespan is sought, by providing an overview of the history, the techniques used and the researchers involved.

750 citations

Frequently Asked Questions (15)
Q1. What contributions have the authors mentioned in the paper "Production-process modelling based on production-management data: a petri-net approach" ?

This paper describes how to apply timed Petri nets and existing production data to the modelling of production systems. The authors describe a method for using these data to construct a Petri-net model algorithmically. This simulator makes it possible to introduce heuristics, and, in this way, various production scenarios can be evaluated. To demonstrate the applicability of their approach, the authors applied it to a scheduling problem in the production of furniture fittings. 

For future work the authors plan to investigate the applicability of highlevel Petri nets to the proposed modelling method as well as the use of the generated models for the testing of various heuristic search algorithms. 

In their work, timed Petri nets with the holding-duration principle of time implementation were used to automate the modelling of a type of production system described by data from production-management systems. 

The product structure given in the form of the BOM and the process structure in the form of routings have also been used by other researchers. 

Soft-computing approaches, e.g. genetic algorithms and neural networks, require considerable computation and only yield sub-optimal solutions. 

Seven of them are related to resources, two invariants refer to the precedence constraints and there are 14 invariants that result from every distinguishable product route. 

So the number of invariants is defined by the sum of resources, the number of product routes and the number of precedences that are present in the model. 

The authors prefer the use of holding durations, because in comparison with firing durations they do not have transitions that remain active over periods of time. 

An interesting property of heuristic dispatching rules is that they can easily be used in conjunction with production models derived within different mathematical modelling frameworks, e.g. the disjunctive graph model (Bła_zewicz et al. 1996, 2000), timed automata (Abdeddaim et al. 2006), and Petri nets (Murata 1989, Zhou and Venkatesh 1999). 

With enabling durations the firing of the transitions happens immediately and the time delays arerepresented by forcing transitions that are enabled to stay so for a specified period of time before they can fire. 

The same timed Petri-net model can also be used in conjunction with other Petri-net scheduling algorithms, e.g. heuristic search. 

It can be stated that the weighted sum of tokens that belongs to every P-invariant, which is a consequence of a resource, is equal to the capacity of that resource. 

From the routing table the function yields the corresponding sequence of production operations and for each operation build a timed Petri net as defined in section 3.2. 

As the role played by information systems in production control increases, the need for a proper evaluation of the various decisions in both the design and operational stages of such systems is becoming more and more important. 

As described by Bowden (2000) there are three basic ways of representing time in Petri nets: firing durations, holding durations and enabling durations.